Quantum geons and noncommutative spacetimes |
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Authors: | A P Balachandran A Ibort G Marmo M Martone |
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Institution: | (1) Department of Humanities and Social Sciences, Polytechnic Institute of New York University, Brooklyn, NY 11201, USA |
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Abstract: | Physical considerations strongly indicate that spacetime at Planck scales is noncommutative. A popular model for such a spacetime
is the Moyal plane. The Poincaré group algebra acts on it with a Drinfel’d-twisted coproduct, however the latter is not appropriate
for more complicated spacetimes such as those containing Friedman-Sorkin (topological) geons. They have rich diffeomorphisms
and mapping class groups, so that the statistics groups for N identical geons is strikingly different from the permutation group S
N
. We generalise the Drinfel’d twist to (essentially all) generic groups including finite and discrete ones, and use it to
deform the commutative spacetime algebras of geons to noncommutative algebras. The latter support twisted actions of diffeomorphisms
of geon spacetimes and their associated twisted statistics. The notion of covariant quantum fields for geons is formulated
and their twisted versions are constructed from their untwisted counterparts. Non-associative spacetime algebras arise naturally in our analysis. Physical consequences, such as the violation of Pauli’s principle, seem
to be one of the outcomes of such nonassociativity. The richness of the statistics groups of identical geons comes from the
nontrivial fundamental groups of their spatial slices. As discussed long ago, extended objects like rings and D-branes also have similar rich fundamental groups. This work is recalled and its relevance to the present quantum geon context
is pointed out. |
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